Nuprl Lemma : comb_for_lookup_wf
λa,B,z,k,xs,z1. (xs[k]) ∈ a:PosetSig ⟶ B:Type ⟶ z:B ⟶ k:|a| ⟶ xs:((|a| × B) List) ⟶ (↓True) ⟶ B
Proof
Definitions occuring in Statement :
lookup: as[k],
list: T List,
squash: ↓T,
true: True,
member: t ∈ T,
lambda: λx.A[x],
function: x:A ⟶ B[x],
product: x:A × B[x],
universe: Type,
set_car: |p|,
poset_sig: PosetSig
Definitions unfolded in proof :
member: t ∈ T,
squash: ↓T,
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
prop: ℙ
Lemmas referenced :
lookup_wf,
squash_wf,
true_wf,
list_wf,
set_car_wf,
poset_sig_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
cut,
lemma_by_obid,
dependent_functionElimination,
thin,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
isectElimination,
productEquality,
universeEquality
Latex:
\mlambda{}a,B,z,k,xs,z1. (xs[k]) \mmember{} a:PosetSig {}\mrightarrow{} B:Type {}\mrightarrow{} z:B {}\mrightarrow{} k:|a| {}\mrightarrow{} xs:((|a| \mtimes{} B) List) {}\mrightarrow{} (\mdownarrow{}True) {}\mrightarrow{} \000CB
Date html generated:
2016_05_16-AM-08_16_39
Last ObjectModification:
2015_12_28-PM-06_27_43
Theory : polynom_2
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